<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>Cindy JS</title>

<script type="text/javascript" src="../build/js/Cindy.js"></script>

<link rel="stylesheet" href="../css/cindy.css">
</head>

<body style="font-family:Arial;">

<h1>Conjugate Scherk Minimal Surface</h1>


<script id='mouseDrag' type='text/x-cindyscript'>
if((mover()!=S) & (mover()!=T),
   xx=mouse().x;
   yy=mouse().y;
   wy=(startx-xx)*.3;
   wx=-(starty-yy)*.3;

   mmmx=[
       [1,0,0],
       [0,cos(wx),sin(wx)],
       [0,-sin(wx),cos(wx)]
       ];


   mmmy=[
       [cos(wy),0,-sin(wy)],
       [0,1,0],
       [sin(wy),0,cos(wy)]
       ];



   mat=mmmx*mmmy*mat;

   startx=mouse().x;
   starty=mouse().y;
   );
</script>

<script id='mouseUp' type='text/x-cindyscript'>

if((mover()!=S) & (mover()!=T),
   xx=mouse().x;
   yy=mouse().y;
   wy=(startx-xx)*.3;
   wx=-(starty-yy)*.3;

   mmmx=[
       [1,0,0],
       [0,cos(wx),sin(wx)],
       [0,-sin(wx),cos(wx)]
       ];


   mmmy=[
       [cos(wy),0,-sin(wy)],
       [0,1,0],
       [sin(wy),0,cos(wy)]
       ];



   mat=mmmx*mmmy*mat;
   );
</script>

<script id='mouseDown' type='text/x-cindyscript'>

startx=mouse().x;
starty=mouse().y;

xx=mouse().x;
yy=mouse().y;
if(xx>14 & xx<21 & yy>-5.5 & yy<-4,newchoice=1);
if(xx>14 & xx<21 & yy>-7.5 & yy<-6,newchoice=2);
if(xx>14 & xx<21 & yy>-9.5 & yy<-8,newchoice=3);


</script>




<script id='init' type='text/x-cindyscript'>



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    [0.09502004679007114,0.9726965834279906,-0.2973738524883489],
    [0.043044633356754514,0.9989629788701292,-0.2552546694679922],
    [-0.08972603070465185,0.9885363607274673,-0.09743050889597143],
    [-0.11455544562527468,0.983736716259986,-0.09323090765527052],
    [-0.09580700313148058,0.9790294361591135,-0.12036541086631272],
    [-0.11550436192642352,0.9717231870685609,-0.11216854373923744],
    [-0.10340856903959034,0.9698306774753215,-0.13955911194871962],
    [-0.11807302846931007,0.9601366595598572,-0.12870706911872812],
    [-0.1119097785372997,0.9603081102914875,-0.15639068644701326],
    [-0.12161977587429222,0.9484066634610014,-0.14355830283010607],
    [-0.12588191701760196,0.9357878878805175,-0.15746269118494016],
    [-0.12131683130654612,0.9496601558531824,-0.1720233498085531],
    [-0.13188620552245203,0.9367742983708767,-0.18728906634813589],
    [-0.13074425147385688,0.9213517897379164,-0.17096547741306933],
    [-0.14377039771729824,0.920057661334564,-0.20254323071690158],
    [-0.13597256528587956,0.9040216907471786,-0.18423920105186659],
    [0.016650373594944083,1.0110229398731518,-0.24744949924950727],
    [0.012514662715799409,1.0175426268377077,-0.27181667281900257],
    [-0.006312065611619788,1.0222060593658633,-0.24459876125244503],
    [-0.004783812599443691,1.030601420744324,-0.2653603059047595],
    [-0.026265286153306904,1.0330184476728201,-0.24457294856392456],
    [-0.020373297252365554,1.04326102250296,-0.26138456202620747],
    [-0.04422623174779837,1.0441670215151613,-0.2462748589731733],
    [-0.03463451762604494,1.0561360493844287,-0.2590017282712097],
    [-0.0612280744555223,1.0565381953751667,-0.2492223412225749],
    [-0.04811334040989619,1.0700114252254012,-0.2576146769864384],
    [-0.07807050323177775,1.0712882550152911,-0.2532589225412795],
    [-0.06123261951813194,1.0858071981935582,-0.2568176049591213],
    [-0.09503640819479556,1.0899958639081415,-0.2582913155898481],
    [-0.0740213686117548,1.104539535709344,-0.2562437624903847],
    [0.0069083808289349714,1.0247826047087565,-0.2924794764409562],
    [.0005553406780352908,1.0329583650471872,-0.31089272103660864],
    [-0.00487910685136912,1.039392501013929,-0.28371994417412344],
    [-0.005854457554540927,1.048847715802466,-0.30046446492890877],
    [-0.015713871098893564,1.0533407277619855,-0.2766789248102585],
    [-0.011742432647823882,1.0635735267859645,-0.2909509166131863],
    [-0.025765072614057114,1.0671944209363877,-0.2707547181626232],
    [-0.017284569484744244,1.0777423170314935,-0.28197791217378004],
    [-0.03535203646183108,1.0816468625573374,-0.2653884227613046],
    [-0.02274109875719266,1.092030277543952,-0.27304515299452375],
    [-0.044762052352154864,1.0974191213013365,-0.260105970033013],
    [-0.028410052796984844,1.1070630649030266,-0.26365959625799357],
    [-0.054073091230938605,1.1151673325616014,-0.2545088585551935],
    [-0.03455105470643735,1.1233353037842557,-0.25344751886990785],
    [-0.006384889821314056,1.0426340543472563,-0.3283416746404994],
    [-0.013914979554872836,1.054788239512273,-0.3458451781394673],
    [-0.00729354445614952,1.0594875060569235,-0.3164474326094776],
    [-0.008875651883393836,1.072076526663524,-0.3323654087212595],
    [-0.008019525724439959,1.0744411787115908,-0.3048147670194476],
    [-0.004148257134885564,1.0865341662671573,-0.3188148082035349],
    [-0.008797734311676146,1.0882740381033777,-0.29321150476613606],
    [.00008684491533742043,1.0992937495310147,-0.30498934832015784],
    [-0.009868240619976662,1.1017446380973965,-0.28113201209021565],
    [0.003713716287460549,1.1112837842789038,-0.2902534439389049],
    [-0.011579307338745341,1.1154840913200172,-0.267999424718375],
    [0.006415620227080427,1.1232021607642435,-0.27379111259543853],
    [-0.01442535144768408,1.1299612578587723,-0.2533775279351953],
    [0.007489022195093072,1.135566823213296,-0.25487137080018113],
    [-0.02181248316610814,1.0709171133622255,-0.364034691156415],
    [-0.010121411856400524,1.0875578730294806,-0.34857143660360246],
    [.00030830284468054935,1.100443423803939,-0.3332691434991865],
    [0.00969459523045146,1.1112218125756983,-0.3177425525774686],
    [0.018299706390755142,1.1209988105346744,-0.3010618938840605],
    [0.02607204680148935,1.1305213675530983,-0.2819784395437286],
    [0.03231902071813071,1.140365495939331,-0.2590887886994989],
    [-0.13646519754626016,0.9781190193254843,-0.09175764033658892],
    [-0.1565823787233703,0.9714712923788559,-0.09184162976750965],
    [-0.1335307668217722,0.9639948782054606,-0.10639164097458374],
    [-0.15037795777611024,0.9555331056984679,-0.10207447778019438],
    [-0.1317225447069846,0.9505840973734618,-0.11958669812548665],
    [-0.14463818412548052,0.940806755945269,-0.11152313006033196],
    [-0.13059714062671265,0.9373690020850557,-0.13176319064414893],
    [-0.13914374138814856,0.9267531120427938,-0.12054772539656232],
    [-0.13363953028514092,0.9127116042692406,-0.12958524943385494],
    [-0.1298551396100667,0.9236775807313352,-0.14343223755065046],
    [-0.12926278749012438,0.9087562470719838,-0.15501805382096734],
    [-0.12787640921581225,0.8980142612948002,-0.13906480265341553],
    [-0.12854275533099072,0.8918810173262341,-0.1667212307528945],
    [-0.12164724922313634,0.8821068108088274,-0.1493303934239999],
    [-0.17609546103806795,0.9632807663100261,-0.09290469529317727],
    [-0.19603799991754323,0.9526377841467992,-0.09463217147768939],
    [-0.1667346117631471,0.9458265085138775,-0.09853309299121138],
    [-0.18320694324918374,0.9341452999895102,-0.09524067759770058],
    [-0.15726766743633638,0.9303203916639788,-0.1038812432559684],
    [-0.17003687241340967,0.9185651097231937,-0.09609892875855937],
    [-0.14764709338954654,0.9160668128927284,-0.1093362063673205],
    [-0.15652045789591607,0.9048472488230356,-0.09756474939168888],
    [-0.14226549438884734,0.8920469351730927,-0.10000806200470932],
    [-0.1376224613909026,0.9023152216021589,-0.1153259524073254],
    [-0.12688951674816207,0.8883819392646684,-0.12234969239703934],
    [-0.1267438319940234,0.8793882793699188,-0.10397871586194266],
    [-0.11525899845133902,0.8737474387436462,-0.13098206568410733],
    [-0.10956468184525653,0.8662977131067094,-0.110342055374906],
    [-0.21705121154969814,0.9380874065087604,-0.09667002890454823],
    [-0.20005029054544463,0.9195595773116721,-0.09166693079868149],
    [-0.1831625529708632,0.9049722132554283,-0.08767858987864553],
    [-0.16611919675939274,0.8927188447465985,-0.084792229024341],
    [-0.14814457942612047,0.8816224421970056,-0.08313842055232097],
    [-0.12822379581131102,0.8708032274519758,-0.0831644081431043],
    [-0.10533763602472287,0.859587010887418,-0.08595060204014049]];



f1 = [[1,2,3,4],[5,2,1,6],[7,2,5,8],[3,2,7,9],[9,7,10,11],[8,12,10,7],[13,10,12,14],[11,10,13,15],[15,13,16,17],[14,18,16,13],[19,20,16,18],[17,16,20,21],[21,20,22,23],[24,22,20,19],[25,22,24,26],[23,22,25,27],[27,25,28,29],[26,30,28,25],[31,28,30,32],[29,28,31,33],[32,34,35,31],[36,37,38,39],[29,33,37,40],[41,40,37,36],[42,40,41,43],[27,29,40,42],[42,44,23,27],[43,45,44,42],[46,47,44,45],[21,23,44,47],[47,48,17,21],[49,48,47,46],[50,48,49,51],[15,17,48,50],[50,52,11,15],[51,53,52,50],[54,55,52,53],[9,11,52,55],[55,56,3,9],[57,56,55,54],[58,56,57,59],[3,56,58,4],[59,60,61,58],[6,1,62,63],[64,65,6,63],[5,6,65,66],[66,65,67,68],[69,67,65,64],[70,71,67,69],[68,67,71,72],[72,71,73,74],[75,73,71,70],[76,73,75,77],[74,73,76,78],[78,76,79,80],[77,81,79,76],[82,83,79,81],[80,79,83,84],[84,83,85,86],[87,85,83,82],[88,85,87,89],[86,85,88,90],[91,92,90,88],[93,94,90,92],[86,90,94,95],[95,94,96,97],[98,96,94,93],[99,100,96,98],[97,96,100,101],[101,100,102,103],[104,102,100,99],[105,106,102,104],[107,103,102,106],[106,108,109,107],[110,108,106,105],[111,112,108,110],[109,108,112,113],[113,112,114,115],[116,114,112,111],[117,118,114,116],[115,114,118,119],[120,119,118,121],[122,123,119,120],[124,115,119,123],[123,125,126,124],[127,125,123,122],[128,129,125,127],[130,126,125,129],[129,131,132,130],[133,131,129,128],[134,135,131,133],[136,132,131,135],[135,137,138,136],[139,137,135,134],[140,141,137,139],[142,138,137,141],[141,32,30,142],[34,32,141,140],[143,36,39,144],[145,41,36,143],[143,146,147,145],[144,148,146,143],[149,146,148,150],[151,147,146,149],[149,152,153,151],[150,154,152,149],[155,152,154,156],[157,153,152,155],[155,158,159,157],[156,160,158,155],[161,158,160,162],[163,159,158,161],[161,164,165,163],[162,166,164,161],[167,164,166,168],[165,164,167,169],[170,171,169,167],[172,169,171,173],[165,169,172,174],[174,172,175,176],[173,177,175,172],[178,175,177,179],[180,176,175,178],[178,181,182,180],[179,183,181,178],[184,181,183,185],[182,181,184,186],[186,184,187,188],[185,189,187,184],[190,187,189,191],[192,188,187,190],[190,193,194,192],[191,195,193,190],[196,197,193,195],[194,193,197,198],[199,198,197,200],[201,198,199,202],[194,198,201,203],[203,201,204,205],[202,206,204,201],[207,208,204,206],[205,204,208,209],[209,208,210,211],[212,210,208,207],[213,210,212,214],[211,210,213,215],[215,213,216,217],[214,218,216,213],[219,216,218,220],[217,216,219,221],[221,219,59,57],[220,60,59,219],[222,66,68,223],[5,66,222,8],[8,222,224,12],[223,225,224,222],[226,224,225,227],[12,224,226,14],[14,226,228,18],[227,229,228,226],[230,231,228,229],[19,18,228,231],[231,232,24,19],[233,232,231,230],[234,232,233,235],[24,232,234,26],[26,234,142,30],[235,138,142,234],[236,221,57,54],[217,221,236,237],[237,236,238,239],[54,53,238,236],[51,240,238,53],[241,239,238,240],[240,242,243,241],[49,242,240,51],[244,242,49,46],[243,242,244,245],[245,244,246,247],[46,45,246,244],[43,248,246,45],[249,247,246,248],[248,145,147,249],[41,145,248,43],[250,215,217,237],[211,215,250,251],[251,250,252,253],[237,239,252,250],[241,254,252,239],[255,253,252,254],[254,256,257,255],[243,256,254,241],[258,256,243,245],[257,256,258,259],[259,258,260,261],[245,247,260,258],[249,262,260,247],[263,261,260,262],[262,151,153,263],[147,151,262,249],[264,209,211,251],[205,209,264,265],[265,264,266,267],[251,253,266,264],[255,268,266,253],[269,267,266,268],[268,270,271,269],[257,270,268,255],[272,270,257,259],[271,270,272,273],[273,272,274,275],[259,261,274,272],[263,276,274,261],[277,275,274,276],[276,157,159,277],[153,157,276,263],[278,203,205,265],[194,203,278,192],[192,278,279,188],[265,267,279,278],[269,280,279,267],[186,188,279,280],[280,281,182,186],[271,281,280,269],[282,281,271,273],[182,281,282,180],[180,282,283,176],[273,275,283,282],[277,284,283,275],[174,176,283,284],[284,163,165,174],[159,163,284,277],[285,72,74,286],[68,72,285,223],[223,285,287,225],[286,288,287,285],[289,287,288,290],[225,287,289,227],[227,289,291,229],[290,292,291,289],[293,294,291,292],[230,229,291,294],[294,295,233,230],[296,295,294,293],[297,295,296,298],[233,295,297,235],[235,297,136,138],[298,132,136,297],[299,78,80,300],[74,78,299,286],[286,299,301,288],[300,302,301,299],[303,301,302,304],[288,301,303,290],[290,303,305,292],[304,306,305,303],[307,308,305,306],[293,292,305,308],[308,309,296,293],[310,309,308,307],[311,309,310,312],[296,309,311,298],[298,311,130,132],[312,126,130,311],[313,84,86,95],[80,84,313,300],[300,313,314,302],[95,97,314,313],[315,314,97,101],[302,314,315,304],[304,315,316,306],[101,103,316,315],[107,317,316,103],[307,306,316,317],[317,318,310,307],[109,318,317,107],[319,318,109,113],[310,318,319,312],[312,319,124,126],[113,115,124,319]] ;

mid=sum(v1)/length(v1);
v1=apply(v1,(#-mid)*6);
use("Cindy3D");

v2=[
[0.06710554787359327,0.9905721936858389,-0.12519391772296426],
[-0.004938155724161591,0.9988790425913484,-0.08682189515702664],
[-0.04300943306947996,0.9982175789310915,-0.12372435824258683],
[-0.006671062871541823,0.991101281283667,-0.1762058620600052],
[0.00970510896140836,1.0049716381415272,-0.042028524624693246],
[0.057101298857496575,1.002847851797516,-0.04468966750071866],
[-0.04211656279914226,0.9991033440546696,-0.06019302946747819],
[-0.025317259251209687,1.0036964837055904,-0.030238516669591424],
[-0.069467706456152,0.9986391458143932,-0.08591165117646019],
[-0.06695577849778162,0.9944993124763515,-0.0385175624509454],
[-0.08918820912718925,0.9940031692486043,-0.05814368716840265],
[-0.05080167589843712,0.9987052736927853,-0.016070025455374427],
[-0.08511966989615888,0.9858210950281622,-0.01994061888530313],
[-0.06951239780903129,0.9901725448949034,-0.0014470472065448957],
[-0.10488190924316426,0.9851630374479786,-0.03647809653680798],
[-0.09881908578985521,0.973174360293457,-0.0034654810188978185],
[-0.11799856782016775,0.9722388004426153,-0.018834823174170068],
[-0.0829631559603207,0.9781675954481533,0.013201571487729633],
[-0.09174798948988104,0.9625478420272982,0.027982428302092997],
[-0.10896796443339041,0.9561928275942942,0.011623318176386324],
[-0.12933928513119114,0.9547780687283693,-0.004108021192302882],
[-0.11573074998696772,0.9339030340621323,0.026037583256013425],
[-0.13941919883635615,0.9315979850172067,0.008338544171666018],
[-0.09569764264556276,0.9429281324755907,0.043351139041307274],
[-0.11847917667795607,0.9042331668268808,0.0408751927198296],
[-0.09369885292715113,0.9187416411813291,0.06026658219848266],
[-0.14867606477257853,0.9002335160211153,0.018923002361547724],
[-0.11489353998855903,0.8622744112486307,0.05870737107423579],
[-0.1575971791975595,0.855857864456993,0.027935983223859127],
[-0.08298780674996442,0.8898132809885961,0.0806533402733719],
[-0.09523858496181159,0.7888816598151428,0.08967343503348009],
[-0.05807241788042474,0.8597601548889602,0.10774621224749151],
[-0.16640602708865615,0.7926522800237391,0.035208185655196664],
[-0.017469379216079182,0.8488702920432627,0.14006424552860092],
[-0.024071142834692236,0.7851110396058177,0.14413868441093458],
[-0.26582940541213357,0.8719732892277084,-0.03776148201870741],
[-0.2418739595996658,0.7975017189972419,-0.013026240749961455],
[-0.317341892111303,0.8023511579718717,-0.06126066715565537],
[-0.31074012849233756,0.8661104104106873,-0.06533510603835439],
[-0.20040730253596623,0.8673013953369256,-0.0011842867913851654],
[-0.22962318227503148,0.8984333402389033,-0.02204633613422737],
[-0.1791714410161654,0.9078010024425781,-0.001632120988863822],
[-0.20460419009832623,0.9252612860882322,-0.0174086868085903],
[-0.1638557531132398,0.9367320947737234,-0.007667941288664983],
[-0.18616394861771404,0.9482462551853399,-0.020009153910801797],
[-0.17154807949187262,0.9672389440603348,-0.027907519083153247],
[-0.1508774653906452,0.9586565058317359,-0.017729027208282185],
[-0.13883136981790273,0.9755265093611265,-0.03148906406960775],
[-0.15943586680119856,0.9826630952658822,-0.04035796442443474],
[-0.12702917156013308,0.9882847733163652,-0.049292964779407575],
[-0.1493124891263973,0.9948636470226299,-0.057336995540372984],
[-0.11508078314249144,0.9973283732973555,-0.07222308809055782],
[-0.1412679846608094,1.0040233966035699,-0.07943032041969045],
[-0.13622260106540926,1.0102161289469014,-0.10791378902485255],
[-0.10280882973750954,1.0026711798578043,-0.10270034505132153],
[-0.09045192260526926,1.0039060269922127,-0.14671355614795437],
[-0.1369302738053703,1.0135916979134914,-0.14472820625420918],
[-0.0795298349541647,0.9991922534598981,-0.22789359941205356],
[-0.15065569986197802,1.015060986942906,-0.19019736983394192],
[-0.1882559269368163,1.0182804101210827,-0.22744666133163902],
[-0.15238860703700813,1.0072832256361597,-0.27958133676426644],
[0.14088215861877765,0.9900431060880147,-0.07418197338586598],
[0.10501483871903333,1.0010402905729237,-0.022047297953428746],
[0.08002087508351174,1.0135260053036106,0.01468725633719365],
[0.04632713562732565,1.0146529073567903,-0.0018418107815822184],
[0.01197455196392927,1.014463174471641,-0.006364019171730944],
[0.03632341666792082,1.0279976195361125,0.02696537377473003],
[0.009148649979728085,1.0265562963904622,0.020485273098029177],
[0.0625579558543321,1.0274897958979443,0.04079299017027645],
[0.049874282908345724,1.0434486608765223,0.060242335813491366],
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[-0.11581663388009598,1.036459956910874,0.13983532921166805]];



f2 = [[1,2,3,4],[5,2,1,6],[7,2,5,8],[3,2,7,9],[9,7,10,11],[8,12,10,7],[13,10,12,14],[11,10,13,15],[15,13,16,17],[14,18,16,13],[19,20,16,18],[17,16,20,21],[21,20,22,23],[24,22,20,19],[25,22,24,26],[23,22,25,27],[27,25,28,29],[26,30,28,25],[31,28,30,32],[29,28,31,33],[32,34,35,31],[36,37,38,39],[29,33,37,40],[41,40,37,36],[42,40,41,43],[27,29,40,42],[42,44,23,27],[43,45,44,42],[46,47,44,45],[21,23,44,47],[47,48,17,21],[49,48,47,46],[50,48,49,51],[15,17,48,50],[50,52,11,15],[51,53,52,50],[54,55,52,53],[9,11,52,55],[55,56,3,9],[57,56,55,54],[58,56,57,59],[3,56,58,4],[59,60,61,58],[6,1,62,63],[64,65,6,63],[5,6,65,66],[66,65,67,68],[69,67,65,64],[70,71,67,69],[68,67,71,72],[72,71,73,74],[75,73,71,70],[76,73,75,77],[74,73,76,78],[78,76,79,80],[77,81,79,76],[82,83,79,81],[80,79,83,84],[84,83,85,86],[87,85,83,82],[88,85,87,89],[86,85,88,90],[91,92,90,88],[93,94,90,92],[86,90,94,95],[95,94,96,97],[98,96,94,93],[99,100,96,98],[97,96,100,101],[101,100,102,103],[104,102,100,99],[105,106,102,104],[107,103,102,106],[106,108,109,107],[110,108,106,105],[111,112,108,110],[109,108,112,113],[113,112,114,115],[116,114,112,111],[117,118,114,116],[115,114,118,119],[120,119,118,121],[122,123,119,120],[124,115,119,123],[123,125,126,124],[127,125,123,122],[128,129,125,127],[130,126,125,129],[129,131,132,130],[133,131,129,128],[134,135,131,133],[136,132,131,135],[135,137,138,136],[139,137,135,134],[140,141,137,139],[142,138,137,141],[141,32,30,142],[34,32,141,140],[143,36,39,144],[145,41,36,143],[143,146,147,145],[144,148,146,143],[149,146,148,150],[151,147,146,149],[149,152,153,151],[150,154,152,149],[155,152,154,156],[157,153,152,155],[155,158,159,157],[156,160,158,155],[161,158,160,162],[163,159,158,161],[161,164,165,163],[162,166,164,161],[167,164,166,168],[165,164,167,169],[170,171,169,167],[172,169,171,173],[165,169,172,174],[174,172,175,176],[173,177,175,172],[178,175,177,179],[180,176,175,178],[178,181,182,180],[179,183,181,178],[184,181,183,185],[182,181,184,186],[186,184,187,188],[185,189,187,184],[190,187,189,191],[192,188,187,190],[190,193,194,192],[191,195,193,190],[196,197,193,195],[194,193,197,198],[199,198,197,200],[201,198,199,202],[194,198,201,203],[203,201,204,205],[202,206,204,201],[207,208,204,206],[205,204,208,209],[209,208,210,211],[212,210,208,207],[213,210,212,214],[211,210,213,215],[215,213,216,217],[214,218,216,213],[219,216,218,220],[217,216,219,221],[221,219,59,57],[220,60,59,219],[222,66,68,223],[5,66,222,8],[8,222,224,12],[223,225,224,222],[226,224,225,227],[12,224,226,14],[14,226,228,18],[227,229,228,226],[230,231,228,229],[19,18,228,231],[231,232,24,19],[233,232,231,230],[234,232,233,235],[24,232,234,26],[26,234,142,30],[235,138,142,234],[236,221,57,54],[217,221,236,237],[237,236,238,239],[54,53,238,236],[51,240,238,53],[241,239,238,240],[240,242,243,241],[49,242,240,51],[244,242,49,46],[243,242,244,245],[245,244,246,247],[46,45,246,244],[43,248,246,45],[249,247,246,248],[248,145,147,249],[41,145,248,43],[250,215,217,237],[211,215,250,251],[251,250,252,253],[237,239,252,250],[241,254,252,239],[255,253,252,254],[254,256,257,255],[243,256,254,241],[258,256,243,245],[257,256,258,259],[259,258,260,261],[245,247,260,258],[249,262,260,247],[263,261,260,262],[262,151,153,263],[147,151,262,249],[264,209,211,251],[205,209,264,265],[265,264,266,267],[251,253,266,264],[255,268,266,253],[269,267,266,268],[268,270,271,269],[257,270,268,255],[272,270,257,259],[271,270,272,273],[273,272,274,275],[259,261,274,272],[263,276,274,261],[277,275,274,276],[276,157,159,277],[153,157,276,263],[278,203,205,265],[194,203,278,192],[192,278,279,188],[265,267,279,278],[269,280,279,267],[186,188,279,280],[280,281,182,186],[271,281,280,269],[282,281,271,273],[182,281,282,180],[180,282,283,176],[273,275,283,282],[277,284,283,275],[174,176,283,284],[284,163,165,174],[159,163,284,277],[285,72,74,286],[68,72,285,223],[223,285,287,225],[286,288,287,285],[289,287,288,290],[225,287,289,227],[227,289,291,229],[290,292,291,289],[293,294,291,292],[230,229,291,294],[294,295,233,230],[296,295,294,293],[297,295,296,298],[233,295,297,235],[235,297,136,138],[298,132,136,297],[299,78,80,300],[74,78,299,286],[286,299,301,288],[300,302,301,299],[303,301,302,304],[288,301,303,290],[290,303,305,292],[304,306,305,303],[307,308,305,306],[293,292,305,308],[308,309,296,293],[310,309,308,307],[311,309,310,312],[296,309,311,298],[298,311,130,132],[312,126,130,311],[313,84,86,95],[80,84,313,300],[300,313,314,302],[95,97,314,313],[315,314,97,101],[302,314,315,304],[304,315,316,306],[101,103,316,315],[107,317,316,103],[307,306,316,317],[317,318,310,307],[109,318,317,107],[319,318,109,113],[310,318,319,312],[312,319,124,126],[113,115,124,319]] ;

mid=sum(v2)/length(v2);
v2=apply(v2,(#-mid)*6);

v3=[
[0.06710554787359313,0.9905721936858396,-0.12519391772296434],
[-0.004938155724252326,0.9988790425913484,-0.08682189515700062],
[0.06924349841434191,1.0001679005412938,-0.014917668549317156],
[0.12018645319269904,0.9901915249562524,-0.08849176835406346],
[-0.04162037205404248,0.9836167419516748,-0.1990318526535012],
[0.0771097968837799,0.978296535581429,-0.20569816789761863],
[-0.10883575557368336,0.9995058683623992,-0.012405709808602046],
[-0.18620370299914257,0.9783525041166348,-0.1503589984462372],
[-0.0024868916189280973,1.0013108004018914,0.08759545414841537],
[-0.2350352080666784,0.9761143784098232,0.09771983131900924],
[-0.09651812657991864,0.9792055524271848,0.2199985673736164],
[-0.3485916059093791,0.946548278884339,-0.060076705250776574],
[-0.36891761734142975,0.9121489739318206,0.2346467654781552],
[-0.5107144320527157,0.8726147281621434,0.06662704095813687],
[-0.2059271533668524,0.9175763502741212,0.3710407797437059],
[-0.4902843843134432,0.8001081891705636,0.38060439124666606],
[-0.31654308996763875,0.808583151068296,0.5198307475733221],
[-0.647384219347873,0.7506354412759126,0.2154679894460442],
[-0.7366447159535409,0.5919270329133245,0.3656525791793584],
[-0.5801959995539556,0.6496642743436183,0.51428007654483],
[-0.4121820883513493,0.6613325983566425,0.6440254128933178],
[-0.6300431412707528,0.4853706577230033,0.6205247457668621],
[-0.48245446480586673,0.4997320513243702,0.7307969619754742],
[-0.7708672846608288,0.42192809080568977,0.4988178821792688],
[-0.6440069465096537,0.3346283261757997,0.6959095065877937],
[-0.7581309014083026,0.2678106167104411,0.6066038913555787],
[-0.5265930253585439,0.35018008379004545,0.7812657439508663],
[-0.6339866387268327,0.21737170440803455,0.7457427526836871],
[-0.5507788468722715,0.22987430839577647,0.8057006223818448],
[-0.7139123356072631,0.1483852517619829,0.6907668375782475],
[-0.6143316815725098,0.14397894503226014,0.7767088199938045],
[-0.6514978529597278,0.07310044174780692,0.7586360406861704],
[-0.5631280189902035,0.1412660533060681,0.8158955628112056],
[-0.5723830676623302,0.05188160716599152,0.8216075410565462],
[-0.48487478428308567,0.06330539252838309,0.8753345874947629],
[-0.5088302328647119,0.1377769713674252,0.8505993433667187],
[-0.46736357132393497,0.20757665524326507,0.8624412986038645],
[-0.3941761122044343,0.12958934268692954,0.9147019321042138],
[-0.4080184990743552,0.3207555864356823,0.8611897952079135],
[-0.2908898474643384,0.2403435368557215,0.9338476064237192],
[-0.33020478712030915,0.4677444581976005,0.8305238802883829],
[-0.17338775087419,0.38680485417377786,0.9172773062528496],
[-0.04674559645448965,0.5513708486170821,0.8488403236021501],
[-0.23454442026793423,0.6293449134850323,0.7563656253202712],
[-0.1278248557043364,0.7788007616450624,0.6344617990277557],
[0.07632356756065747,0.7080917916013881,0.7223344622144411],
[-0.02326604414710197,0.8918296133518455,0.4767323101115468],
[0.1791846744464519,0.8320585444610112,0.5498147765397474],
[0.06480313620497423,0.9584881793365906,0.3077189591228022],
[0.2488879068340037,0.91142504321567,0.3583827045119149],
[0.2810373286563299,0.9508854252821152,0.17688470146439048],
[0.12715268132772545,0.9856331291044692,0.15287457164814328],
[0.1616849029363633,0.9890839938267164,0.02987664481809913],
[0.27811583341998475,0.9648208336971884,0.02490322967982148],
[0.1726069905849842,0.9843702202954564,-0.05130339842775344],
[0.24373285543452783,0.9685014868254406,-0.08899962797499876],
[0.17046904001194793,0.9747745134489916,-0.16157964754466494],
[0.2382295748522567,0.9409247919581326,-0.261169815881178],
[0.10721893241870732,0.9453065009738006,-0.325439432047528],
[-0.050989345230710095,0.944432700235208,-0.3462661275765532],
[0.15804436367787972,0.8775066403124221,-0.471798759451549],
[-0.03298256477707359,0.8673747581665718,-0.5173510816684611],
[0.3214962075913897,0.8743426926077694,-0.3856470881482682],
[0.4099207532706628,0.7630850631110878,-0.5212386915880465],
[0.2241688777570943,0.7633676028864778,-0.624654528911487],
[0.011813197622881182,0.7415337178426655,-0.6904440969132882],
[0.2955408010148723,0.6029764909061809,-0.7579489300591982],
[0.07862635483333356,0.5685088057937524,-0.8364221310997415],
[0.4883228324269842,0.6066749030809914,-0.6463100023530367],
[0.3611248204996204,0.41352502300431065,-0.8495651731573375],
[0.5436203761086329,0.4215604888629243,-0.7408017634057567],
[0.15826686521161687,0.3674299797293882,-0.9309520221385787],
[0.41409840708845824,0.22343785328752272,-0.892293690468689],
[0.24074710657424517,0.16815503276739863,-0.966873145390325],
[0.5716698230558274,0.23529498167184223,-0.79648510225893],
[0.5779683171205399,0.07309040217198276,-0.8190927209185698],
[0.4541303143239347,0.05915018668094506,-0.8951413397026177],
[0.3197481934252317,-0.0025855691050447687,-0.9550956384100772],
[0.4848747949685769,-0.06330528933823155,-0.8753345889440411],
[0.3941761273879884,-0.12958923948126524,-0.9147019401080038],
[0.5723830758691872,-0.051881504052140114,-0.8216075417363585],
[0.5088302470180427,-0.13777686805917264,-0.8505993516203881],
[0.5631280326468174,-0.14126594995429675,-0.815895571252625],
[0.4673635894125275,-0.20757655297700173,-0.8624413134136596],
[0.5507788658250299,-0.22987420649379792,-0.8057006385081008],
[0.5265930511796024,-0.3501799866359505,-0.7812657702835901],
[0.4080185223483034,-0.32075548819964766,-0.8611898209279361],
[0.2908898672005263,-0.24034343589923063,-0.9338476263394956],
[0.3302048150121354,-0.4677443696870208,-0.8305239196675412],
[0.17338777300899094,-0.386804760693632,-0.9172773420066654],
[0.4824544981188629,-0.4997319647480095,-0.7307969998941484],
[0.4121821273404856,-0.6613325294685704,-0.6440254604020678],
[0.2345444499031186,-0.629344841900657,-0.7563656771842032],
[0.04674561667416388,-0.5513707699640308,-0.8488403749232348],
[0.12782488258264416,-0.7788007121736741,-0.6344618570506532],
[-0.07632355413665937,-0.7080917339224392,-0.7223345226979134],
[0.3165431300462699,-0.8085831046895761,-0.519830798527155],
[0.20592718898003448,-0.9175763255480792,-0.3710408261376588],
[0.023266064314723486,-0.8918295856546832,-0.4767323650021161],
[-0.1791846705617449,-0.832058508841638,-0.5498148355999437],
[-0.06480312410478394,-0.9584881677169854,-0.3077190032663534],
[-0.24888791157932463,-0.911425025126656,-0.3583827526479929],
[0.09651815397503104,-0.9792055432535016,-0.2199986033376197],
[0.0024869100957163304,-1.0013107993035733,-0.0875954780550656],
[-0.1271526759132157,-0.9856331262035803,-0.15287460211155715],
[-0.28103733843445594,-0.9508854178264866,-0.17688473415019307],
[-0.16168490145881442,-0.9890839940771892,-0.02987666297370217],
[-0.2781158439243689,-0.9648208311614545,-0.024903247312697163],
[-0.06924348736931388,-1.000167902062595,0.014917655035246134],
[-0.1201864475528698,-0.990191526449914,0.08849176256058144],
[-0.17260699040069943,-0.9843702209829346,0.05130338872964167],
[-0.24373286274366265,-0.9685014860888028,0.0889996222392262],
[-0.17046903971297786,-0.9747745137584748,0.16157964947722137],
[-0.23822958150666215,-0.9409247880258595,0.2611698280982393],
[-0.343207386331136,-0.9314337562861372,0.16015915236172368],
[-0.4162517099786117,-0.9169656123915898,0.01902241478134797],
[-0.4578827346430422,-0.8598804252451149,0.26179964326591404],
[-0.5644969828893579,-0.8322515010058991,0.09889166714690112],
[-0.3214962218451604,-0.8743426787376994,0.38564711204991714],
[-0.40992077329430415,-0.7630850321115631,0.5212387251662869],
[-0.569820483553326,-0.7430482086591573,0.3825690052366115],
[-0.7017123444364978,-0.7009774935380312,0.207256365802524],
[-0.6580003611133737,-0.5816690073275091,0.504091548152402],
[-0.8023341781387251,-0.5259650928221967,0.3295556694593142],
[-0.4883228535780615,-0.6066748497977048,0.6463100394111314],
[-0.5436203927560446,-0.4215604137014145,0.7408017958680319],
[-0.7067764229192565,-0.3932055846108603,0.6074796483671372],
[-0.8481660086902183,-0.3268737117959346,0.44776428992568257],
[-0.7139367721407132,-0.20581156087692956,0.6822945723295649],
[-0.8382266484039239,-0.13303169925232566,0.5484137289400227],
[-0.5716698313920974,-0.2352948903988396,0.796485124205186],
[-0.5779683164307867,-0.07309030218346323,0.8190927307092061],
[-0.6901187609106022,-0.045277346175892935,0.7298610575966417],
[-0.7869892414086945,0.030052751469699216,0.6278519232273153],
[-0.4541303087249057,-0.05915008611983471,0.8951413495301757],
[-0.3197481815784946,0.002585671362407604,0.9550956424011942],
[-0.4140984070093411,-0.22343776087354117,0.8922937145105411],
[-0.2407470970484678,-0.16815493663820447,0.9668731652684588],
[-0.3611248245335079,-0.4135249462891,0.8495652104652321],
[-0.15826685560468645,-0.36742989753363,0.930952057776366],
[-0.2955408059670574,-0.6029764359919015,0.7579489744440927],
[-0.07862634227787701,-0.5685087445977165,0.8364221763742817],
[-0.22416888004397623,-0.7633675705398918,0.6246545710156407],
[-0.011813180415560195,-0.74153367970783,0.6904441415087414],
[-0.1580443612027536,-0.8775066255700524,0.47179879141635855],
[0.032982586166216334,-0.8673747390912425,0.5173511161909342],
[-0.10721892528542838,-0.9453064965803056,0.32543945066040403],
[0.05098936859883113,-0.9444326932398638,0.3462661474230862],
[-0.0771097867139358,-0.9782965355988772,0.20569817433038248],
[0.041620394558560245,-0.9836167408325736,0.19903185804672277],
[-0.06710553664939849,-0.9905721948471428,0.12519391572590427],
[0.004938174460973248,-0.998879043578637,0.08682188906500742],
[0.10883578472256968,-0.9995058664654995,0.012405695991504736],
[0.1862037396350996,-0.9783524986347784,0.15035899824908652],
[0.23503524838800183,-0.9761143679674626,-0.09771985556838846],
[0.3485916559603779,-0.9465482630927288,0.06007669567229512],
[0.36891766617575095,-0.9121489474056912,-0.2346468000100591],
[0.5107144905610087,-0.872614694783244,-0.06662706127730439],
[0.4902844354393826,-0.800108140657788,-0.3806044318518828],
[0.6473842775002803,-0.7506353853652444,-0.21546801779971775],
[0.5801960456733258,-0.649664203372957,-0.5142801163345501],
[0.7366447647969224,-0.5919269553107454,-0.365652609442131],
[0.63004317762676,-0.485370569485475,-0.62052477868781],
[0.7708673195059222,-0.4219279976968112,-0.4988179079978665],
[0.6440069724507311,-0.33462822797956643,-0.6959095299887318],
[0.7581309229823491,-0.2678105156876744,-0.6066039090983945],
[0.6339866565904799,-0.21737160207842732,-0.7457427673203794],
[0.7139123479428325,-0.14838514833202773,-0.6907668469417011],
[0.6143316947732606,-0.14397884164899932,-0.7767088287021326],
[0.6514978608728841,-0.0731003383849863,-0.7586360437393054],
[0.6901187596762021,0.04527744710489216,-0.729861052077207],
[0.7869892433210293,-0.030052648640903176,-0.6278519252750858],
[0.713936758722528,0.2058116539602906,-0.682294557149081],
[0.8382266355028164,0.13303179651810462,-0.5484137236372014],
[0.7067763971706548,0.3932056623516426,-0.6074796256313101],
[0.84816597974871,0.32687379582392034,-0.447764280086688],
[0.6580003273350539,0.5816690635608839,-0.5040915233722139],
[0.8023341375185971,0.5259651564517043,-0.3295556603501883],
[0.5698204493044413,0.7430482424363558,-0.3825689850661173],
[0.7017123012245513,0.700977534369519,-0.20725636271695025],
[0.4578827070023974,0.8598804413137447,-0.26179963210095764],
[0.5644969464506283,0.8322515226171492,-0.09889167263051107],
[0.3432073689105111,0.931433761748084,-0.16015915078683454],
[0.416251685916909,0.916965621440636,-0.019022427908715347],
[-0.23445415507262557,0.9279428113124236,-0.32248548818823203],
[-0.2491839103633052,0.8349680141047627,-0.5171557684990761],
[-0.4330118895007189,0.8810830056979141,-0.25081414502769034],
[-0.4788892144298144,0.7676873762042516,-0.46344665099760224],
[-0.6247297120268882,0.7904121159738818,-0.1318343671646185],
[-0.6970706798536292,0.6555826924793616,-0.3514920483247977],
[-0.7795738138576349,0.6529918190964697,0.02393586549962747],
[-0.869641991662913,0.5000700715164116,-0.18765938530767448],
[-0.9683558332935582,0.31854773157769867,0.007562011422765879],
[-0.8723254766844155,0.48280800438433336,0.19586608049495405],
[-0.8956557679905197,0.3063108127350372,0.3615089598233047],
[-0.9856146341196096,0.13814985212044273,0.20721968962889817],
[-0.8608314062389664,0.1497541271095511,0.5065436758156358],
[-0.93488954979859,-0.01692814105963746,0.3903962927546294],
[0.45479796988073423,0.8874246608160872,0.1602491183563784],
[0.634992175811665,0.7829911273020801,0.1020986084069954],
[0.45116419798078056,0.8291061187924073,0.36844023250260255],
[0.657142515614694,0.7009049858044505,0.3322009942551247],
[0.397409747372638,0.7303249594015471,0.584046036581253],
[0.6172514581588977,0.5783193805005936,0.5690256504567376],
[0.292992364990819,0.5899402939880176,0.7751338569827738],
[0.5098552809469915,0.4189753955505352,0.7785053148835805],
[0.1498140038229812,0.4227208468458229,0.911746498597024],
[0.34596633445734576,0.24128441823784835,0.9280797304302154],
[-0.01147964639182522,0.2543339242679252,0.980763360557174],
[0.15041714393729827,0.07136745952319148,1.0028673675362294],
[-0.1715792452768922,0.10923597496509914,0.989278306849542],
[-0.05071341305671557,-0.06890503017670736,1.0096507040516391],
[0.7971409375476399,0.6300485999952182,0.004890155511730015],
[0.911601395979824,0.4347563535016144,-0.1211461112987346],
[0.8400539659868547,0.5224272588983855,0.2462152566419825],
[0.967265466941452,0.30422971404933846,0.1157804481174548],
[0.8116693966781457,0.3756200615431405,0.4951754280952698],
[0.9471322291121608,0.1377217226333264,0.3625194282786277],
[0.7021444366053297,0.19917923261660855,0.7174732690445416],
[0.83826826918325,-0.04927811264492543,0.5871016987607448],
[0.5216030691064558,0.01525199078643176,0.8790870047741627],
[0.6498575610102111,-0.23160174354686283,0.7559714632846094],
[0.29841437717202296,-0.15048646346901706,0.9630916605044928],
[0.41223183724091605,-0.3853243046250081,0.8503842725815729],
[0.06450077032231444,-0.28015742443692665,0.974561592909412],
[0.16096480559507917,-0.497807806392296,0.8723441384579801],
[0.9576387244920193,0.2200703578220753,-0.25868115197563546],
[0.934889544979461,0.016928242848295083,-0.3903962981946285],
[1.0159078090226967,0.0732232492134706,-0.04257393639465257],
[0.985614645480084,-0.13814974895214674,-0.2072197032499792],
[0.9996976913161922,-0.10468257625190155,0.186393215495362],
[0.9683558658457678,-0.31854763408421577,-0.007562026599026299],
[0.8948453591900768,-0.2930592541698389,0.40101761436459177],
[0.8696420430112368,-0.5000699883560658,0.187659377390829],
[0.7096313623003179,-0.4650506659015858,0.5703047926510797],
[0.697070739621955,-0.6555826293416682,0.3514920542078623],
[0.4742682176855082,-0.599690506148592,0.6743024683015331],
[0.4788892693952101,-0.7676873328905328,0.46344667148763447],
[0.22499855415302367,-0.6901357073426159,0.710990286451277],
[0.2491839506655885,-0.8349679858652514,0.5171557992498258],
[0.8608314175661146,-0.1497540237035851,-0.5065436868197869],
[0.8956557947580278,-0.30631071345044747,-0.36150897833529455],
[0.8723255215128739,-0.4828079169022959,-0.195866101533242],
[0.7795738727545843,-0.6529917509572799,-0.02393588181298341],
[0.6247297748494801,-0.7904120701905746,0.1318343615115447],
[0.4330119449400261,-0.8810829792098311,0.2508141515188838],
[0.2344541956731213,-0.9279427976554748,0.322485503899244],
[-0.22499851856775585,0.6901357563090853,-0.710990246664812],
[-0.16096477753545615,0.4978078781901192,-0.8723441002334742],
[-0.4742681696717251,0.5996905706918708,-0.6743024410152774],
[-0.4122318005964076,0.385324389615744,-0.8503842496508892],
[-0.7096313134260657,0.4650507480237499,-0.5703047830845592],
[-0.649857527698217,0.23160184037665077,-0.7559714607987079],
[-0.8948453233501427,0.2930593506076883,-0.40101762153460113],
[-0.8382682521294151,0.04927821491973951,-0.5871017146446735],
[-0.9471322353961532,-0.13772162399149354,-0.3625194527220496],
[-0.9996976778023652,0.1046826789514134,-0.18639323143734657],
[-1.0159078178615926,-0.07322314895825041,0.04257392246555764],
[-0.9672654941571444,-0.3042296261361552,-0.11578046861871824],
[-0.9576387482517774,-0.22007026526464052,0.25868114825372124],
[-0.91160143506997,-0.43475627863081295,0.1211461038538732],
[-0.06450074937837284,0.28015751483794543,-0.9745615669062956],
[0.05071343010617344,0.06890513078563637,-1.0096506957159117],
[-0.29841435165049524,0.1504865619959111,-0.9630916520210244],
[-0.15041712495010465,-0.07136735695573891,-1.0028673775139754],
[-0.5216030497460042,-0.015251888547407322,-0.8790870179238838],
[-0.34596632210974954,-0.24128432013112677,-0.9280797612574504],
[-0.7021444340710571,-0.1991791348621488,-0.7174733001404167],
[-0.5098552833143799,-0.4189753102668779,-0.7785053613873459],
[-0.617251478071749,-0.5783193140278043,-0.5690257006758829],
[-0.811669415566486,-0.3756199765130367,-0.49517546579911126],
[-0.8400540023623948,-0.5224271906492938,-0.2462152877061379],
[-0.6571425490470065,-0.7009049386972102,-0.3322010354300091],
[-0.7971409821757537,-0.6300485474687819,-0.0048901709580463325],
[-0.6349922147741718,-0.782991095614151,-0.10209863266225602],
[0.17157926232375448,-0.10923587200971908,-0.9892783151222244],
[0.011479664741820729,-0.2543338248633283,-0.9807633864202095],
[-0.14981399042360624,-0.4227207582529312,-0.9117465430188528],
[-0.29299236257670513,-0.589940223615968,-0.7751339138702588],
[-0.3974097581946237,-0.7303249105753815,-0.5840460943296145],
[-0.4511642191931771,-0.8291060890615234,-0.36844027976934607],
[-0.4547979955772581,-0.887424644313926,-0.16024914889268613],
[0.5723830758691872,-0.051881504052140114,-0.8216075417363585],
[0.5631280326468174,-0.14126594995429675,-0.815895571252625],
[0.4824544981188629,-0.4997319647480095,-0.7307969998941484],
[0.5265930511796024,-0.3501799866359505,-0.7812657702835901],
[0.0024869100957163304,-1.0013107993035733,-0.0875954780550656],
[0.17046904001194793,0.9747745134489916,-0.16157964754466494],
[0.2382295748522567,0.9409247919581326,-0.261169815881178],
[-0.23822958150666215,-0.9409247880258595,0.2611698280982393],
[-0.17046903971297786,-0.9747745137584748,0.16157964947722137],
[-0.1201864475528698,-0.990191526449914,0.08849176256058144],
[-0.06924348736931388,-1.000167902062595,0.014917655035246134],
[-0.1201864475528698,-0.990191526449914,0.08849176256058144],
[0.4883228324269842,0.6066749030809914,-0.6463100023530367],
[0.4121821273404856,-0.6613325294685704,-0.6440254604020678],
[0.3165431300462699,-0.8085831046895761,-0.519830798527155],
[0.5507788658250299,-0.22987420649379792,-0.8057006385081008],
[0.5631280326468174,-0.14126594995429675,-0.815895571252625],
[0.4099207532706628,0.7630850631110878,-0.5212386915880465],
[0.3214962075913897,0.8743426926077694,-0.3856470881482682],
[-0.5716698313920974,-0.2352948903988396,0.796485124205186],
[-0.5436203927560446,-0.4215604137014145,0.7408017958680319],
[0.5631280326468174,-0.14126594995429675,-0.815895571252625],
[-0.1201864475528698,-0.990191526449914,0.08849176256058144],
[0.5436203761086329,0.4215604888629243,-0.7408017634057567],
[0.12018645319269904,0.9901915249562524,-0.08849176835406346],
[0.12018645319269904,0.9901915249562524,-0.08849176835406346],
[-0.3214962218451604,-0.8743426787376994,0.38564711204991714],
[-0.5631280189902035,0.1412660533060681,0.8158955628112056],
[0.20592718898003448,-0.9175763255480792,-0.3710408261376588],
[0.09651815397503104,-0.9792055432535016,-0.2199986033376197],
[-0.5779683164307867,-0.07309030218346323,0.8190927307092061],
[-0.5723830676623302,0.05188160716599152,0.8216075410565462],
[-0.5631280189902035,0.1412660533060681,0.8158955628112056],
[-0.4883228535780615,-0.6066748497977048,0.6463100394111314],
[-0.40992077329430415,-0.7630850321115631,0.5212387251662869],
[0.5716698230558274,0.23529498167184223,-0.79648510225893],
[0.5779683171205399,0.07309040217198276,-0.8190927209185698]];



f3 = [[1,2,3,307],[5,2,1,6],[7,2,5,8],[3,2,7,9],[9,7,10,11],[8,12,10,7],[13,10,12,14],[11,10,13,15],[15,13,16,17],[14,18,16,13],[19,20,16,18],[17,16,20,21],[21,20,22,23],[24,22,20,19],[25,22,24,26],[23,22,25,27],[27,25,28,29],[26,30,28,25],[31,28,30,32],[29,28,31,315],[32,34,310,31],[35,36,33,314],[29,315,36,37],[38,37,36,35],[39,37,38,40],[27,29,37,39],[39,41,23,27],[40,42,41,39],[43,44,41,42],[21,23,41,44],[44,45,17,21],[46,45,44,43],[47,45,46,48],[15,17,45,47],[47,49,11,15],[48,50,49,47],[51,52,49,50],[9,11,49,52],[52,53,3,9],[54,53,52,51],[55,53,54,56],[3,53,55,307],[56,288,4,55],[6,1,308,57],[58,59,6,57],[5,6,59,60],[60,59,61,62],[301,61,59,58],[300,65,61,301],[62,61,65,66],[66,65,67,68],[69,67,65,300],[70,67,69,71],[68,67,70,72],[72,70,73,74],[71,75,73,70],[76,77,73,75],[74,73,77,78],[78,77,79,80],[81,79,77,76],[82,79,81,304],[80,79,82,84],[299,298,84,82],[286,87,84,298],[80,84,87,88],[88,87,89,90],[285,89,87,286],[92,93,89,285],[90,89,93,94],[94,93,95,96],[97,95,93,92],[98,99,95,97],[100,96,95,99],[99,101,102,100],[103,101,99,98],[104,105,101,103],[102,101,105,106],[106,105,107,108],[109,107,105,104],[110,111,107,109],[108,107,111,112],[291,112,111,292],[114,115,112,291],[116,108,112,115],[115,117,118,116],[309,117,115,114],[317,121,117,309],[122,118,117,121],[121,123,124,122],[316,123,121,317],[303,127,123,316],[128,124,123,127],[127,129,130,128],[302,129,127,303],[132,133,129,302],[134,130,129,133],[133,32,30,134],[34,32,133,132],[135,35,314,313],[136,38,35,135],[135,137,138,136],[313,131,137,135],[139,137,131,126],[140,138,137,139],[139,141,142,140],[126,125,141,139],[143,141,125,120],[144,142,141,143],[143,145,146,144],[120,119,145,143],[147,145,119,290],[148,146,145,147],[147,149,150,148],[290,113,149,147],[151,149,113,294],[150,149,151,152],[305,293,152,151],[153,152,293,287],[150,152,153,154],[154,153,155,156],[287,312,155,153],[157,155,312,311],[158,156,155,157],[157,159,160,158],[311,297,159,157],[161,159,297,296],[160,159,161,162],[162,161,163,164],[296,91,163,161],[165,163,91,86],[166,164,163,165],[165,167,168,166],[86,85,167,165],[284,169,167,85],[168,167,169,170],[283,170,169,83],[171,170,283,319],[168,170,171,172],[172,171,173,174],[319,318,173,171],[306,175,173,318],[174,173,175,176],[176,175,177,178],[295,177,175,306],[179,177,295,64],[178,177,179,180],[180,179,181,182],[64,63,181,179],[183,181,63,289],[182,181,183,184],[184,183,56,54],[289,288,56,183],[185,60,62,186],[5,60,185,8],[8,185,187,12],[186,188,187,185],[189,187,188,190],[12,187,189,14],[14,189,191,18],[190,192,191,189],[193,194,191,192],[19,18,191,194],[194,195,24,19],[196,195,194,193],[197,195,196,198],[24,195,197,26],[26,197,134,30],[198,130,134,197],[199,184,54,51],[182,184,199,200],[200,199,201,202],[51,50,201,199],[48,203,201,50],[204,202,201,203],[203,205,206,204],[46,205,203,48],[207,205,46,43],[206,205,207,208],[208,207,209,210],[43,42,209,207],[40,211,209,42],[212,210,209,211],[211,136,138,212],[38,136,211,40],[213,180,182,200],[178,180,213,214],[214,213,215,216],[200,202,215,213],[204,217,215,202],[218,216,215,217],[217,219,220,218],[206,219,217,204],[221,219,206,208],[220,219,221,222],[222,221,223,224],[208,210,223,221],[212,225,223,210],[226,224,223,225],[225,140,142,226],[138,140,225,212],[227,176,178,214],[174,176,227,228],[228,227,229,230],[214,216,229,227],[218,231,229,216],[232,230,229,231],[231,233,234,232],[220,233,231,218],[235,233,220,222],[234,233,235,236],[236,235,237,238],[222,224,237,235],[226,239,237,224],[240,238,237,239],[239,144,146,240],[142,144,239,226],[241,172,174,228],[168,172,241,166],[166,241,242,164],[228,230,242,241],[232,243,242,230],[162,164,242,243],[243,244,160,162],[234,244,243,232],[245,244,234,236],[160,244,245,158],[158,245,246,156],[236,238,246,245],[240,247,246,238],[154,156,246,247],[247,148,150,154],[146,148,247,240],[248,66,68,249],[62,66,248,186],[186,248,250,188],[249,251,250,248],[252,250,251,253],[188,250,252,190],[190,252,254,192],[253,255,254,252],[256,257,254,255],[193,192,254,257],[257,258,196,193],[259,258,257,256],[260,258,259,261],[196,258,260,198],[198,260,128,130],[261,124,128,260],[262,72,74,263],[68,72,262,249],[249,262,264,251],[263,265,264,262],[266,264,265,267],[251,264,266,253],[253,266,268,255],[267,269,268,266],[270,271,268,269],[256,255,268,271],[271,272,259,256],[273,272,271,270],[274,272,273,275],[259,272,274,261],[261,274,122,124],[275,118,122,274],[276,78,80,88],[74,78,276,263],[263,276,277,265],[88,90,277,276],[278,277,90,94],[265,277,278,267],[267,278,279,269],[94,96,279,278],[100,280,279,96],[270,269,279,280],[280,281,273,270],[102,281,280,100],[282,281,102,106],[273,281,282,275],[275,282,116,118],[106,108,116,282]]  ;

mid=sum(v3)/length(v3);
v3=apply(v3,(#-mid)*1.2);


mat=[
    [1,0,0],
    [0,1,0],
    [0,0,1]
    ];
mat=[[0.56,0.49,-0.67],[-0.52,-0.42,-0.74],[-0.65,0.76,0.02]];
mat0=[
    [1,0,0],
    [0,1,0],
    [0,0,1]
    ];



mmmx=mat0;
mmmy=mat0;

choice=1;
newchoice=1;
animstate=1;


</script>


<script id='tick' type='text/x-cindyscript'>
animstate=animstate+0.1;
errc(animstate);
if(animstate>=1,
 animstate=1;
 javascript("cdy.stop()");
);
if(animstate>=0,
  choice=newchoice
);

</script>



<script id='csmove' type='text/x-cindyscript'>
if((choice!=newchoice) & (animstate==1),
  animstate=-1;
  errc(animstate);

  javascript("cdy.play()");

);

if(choice==1,v=v2;f=f2;);
if(choice==2,v=v1;f=f1;);
if(choice==3,v=v3;f=f3;);

fillpolygon([(14,-4),(14,-5.5),(21,-5.5),(21,-4)],color->(.6,.6,1)*if(newchoice==1,0.7,1.1));
drawpolygon([(14,-4),(14,-5.5),(21,-5.5),(21,-4)],color->(0,0,0));

fillpolygon([(14,-6),(14,-7.5),(21,-7.5),(21,-6)],color->(.6,.6,1)*if(newchoice==2,0.7,1.1));
drawpolygon([(14,-6),(14,-7.5),(21,-7.5),(21,-6)],color->(0,0,0));

fillpolygon([(14,-8),(14,-9.5),(21,-9.5),(21,-8)],color->(.6,.6,1)*if(newchoice==3,0.7,1.1));
drawpolygon([(14,-8),(14,-9.5),(21,-9.5),(21,-8)],color->(0,0,0));

drawtext((15,-5),"Sherk Tower");
drawtext((15,-7),"Conjugate");
drawtext((15,-9),"Gauss map");


fillpolygon([(31,-.8),(31,-2.5),(35,-2.5),(35,-.8)],color->(.6,.6,1)*if(!grid,1.1,0.7));
drawpolygon([(31,-.8),(31,-2.5),(35,-2.5),(35,-.8)],color->(0,0,0));
drawtext((31.5,-2),"Cells");


y=S.y;
if(y<S1.y,y=S1.y);
if(y>S2.y,y=S2.y);

S.xy=(S1.x,y);

s1=(|S,S1|/|S1,S2|);


y=T.y;
if(y<T1.y,y=T1.y);
if(y>T2.y,y=T2.y);

T.xy=(T1.x,y);

al=(|T,T1|/|T1,T2|);

vv=apply(v,mat*#);

f=sort(f,fa,sum(fa,p,(vv_p)_3));

s1=3*exp(s1*5);
scale=|sin(animstate*pi/2)|;

mapt(pt):=[pt_1,#_2]/(s1-#_3)*s1*6*scale+(2,2);

apply(f,q,
      pol=apply(q,vv_#);
      d=sum(pol)_3*.2+1.0;
      n=cross(pol_1-pol_3,pol_2-pol_4);
      n=n/|n|;
      col=(0.4,0.4,.7);
      col=col+max(((n*(1,5,5)),0))*(.8,.6,.6)*.1;
      col=col+max(((n*(-1,5,5)),0))*(.6,.4,.6)*.1;
      pol=apply(pol,mapt(#));
      fillpoly(pol,color->(col-(0.5,0.5,0))*d,alpha->al);
      pol=pol++[pol_1];
      forall(1..4,draw(pol_#,pol_(#+1),size->2*scale,color->col*d*.02));

      );

drawtext(S1-(1.8,1),size->16,"perspective");
drawtext(T1-(1,1),size->16,"alpha");


</script>


<script id='timer' type='text/x-cindyscript'>



</script>

<div  id="CSCanvas" style="width:800px; height:600px; border:2px solid #000000"></div>

<script type="text/javascript">

var gslp=[
    {name:"A", kind:"P", type:"Free",alpha:0, pos:[-1000,-1000,1],alpha:.001} ,
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    {name:"S2", type:"Free", pos:[16,12],color:[0,0,0],pinned:true,size:2},
    {name:"S", type:"Free", pos:[16,3.5],color:[1,0.5,0.5],pinned:false,size:4,narrow:true},
    {name:"l", type:"Segment", args:["S1","S2"],color:[0,0,0],pinned:false,size:2},
     {name:"T1", type:"Free", pos:[20,-2],color:[0,0,0],pinned:true,size:2},
    {name:"T2", type:"Free", pos:[20,12],color:[0,0,0],pinned:true,size:2},
    {name:"T", type:"Free", pos:[20,8.5],color:[1,0.5,0.5],pinned:false,size:4,narrow:true},
    {name:"m", type:"Segment", args:["T1","T2"],color:[0,0,0],pinned:false,size:2}


    ];

var cdy = CindyJS({canvasname:"CSCanvas",
movescript:"csmove",
initscript:"init",
mousedownscript:"mouseDown",
mouseupscript:"mouseUp",
tickscript:"tick",
mousedragscript:"mouseDrag",
geometry:gslp
}

);


</script>

</body>
</html>
